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Additional info for Advanced Calculus of real valued functions of real variable and vectored valued functions of a vector 0
In the analysis, we compared the performance of prediction models using data sets with and without explicit representations of the absence of data elements. 1 Synthetic Data Whittaker reports a data set  that involves six boolean risk factors X1 , . . , X6 observed in a sample of 1841 employees of a Czech car factory. Ramoni and Sebastiani  considered these data and used a structure learning algorithm to output Exploiting Data Missingness in Bayesian Network Modeling 41 a structure that they used afterwards as a toy problem to learn the conditional probability tables from incomplete data sets.
Detecting fuzzy communities in complex networks with a potts model. Phys. Rev. Lett. 93 (2004) 20. : Deﬁning and identifying communities in networks. Publ. Natl. Acad. Sci. USA 101, 2658–2663 (2004) 21. : Optimization by simulated annealing. Science 220, 671 (1983) 22. : Community structure in social and biological networks. hk Abstract. Data streams are dynamic, with frequent distributional changes. In this paper, we propose a statistical approach to detecting distributional shifts in multi-dimensional data streams.
U is composed by all the original random variables (Xi ) and artiﬁcially created variables (Ri ) representing missingness of their respective random variables. MBLearning is then ﬁrst run on the target variable T (line 2). It is then run again repeatedly on the adjacent nodes and so on up to a radius of r around the target node (lines 5-13). A similar approach was proposed in , but it does not take into account missingness as a possible piece of information. After ﬁnishing the feature subset selection process, GMB creates at line 14 the local BN including the selection of existing and the dummy variables.